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(B) Given $y = \sin(e^{\log 2x})$.Using the property $e^{\log_e f(x)} = f(x)$, we simplify the expression:$y = \sin(2x)$.Now, differentiate with respe

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$-2$

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(B) Given $y = \sin(e^{\log 2x})$.Using the property $e^{\log_e f(x)} = f(x)$, we simplify the expression:$y = \sin(2x)$.Now, differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(\sin(2x)) = \cos(2x) \cdot \frac{d}{dx}(2x) = 2\cos(2x)$.Substitute $x = \frac{\pi}{2}$ into the derivative:$\frac{dy}{dx} = 2\cos(2 \cdot \frac{\pi}{2}) = 2\cos(\pi)$.Since $\cos(\pi) = -1$, we get:$\frac{dy}{dx} = 2(-1) = -2$.

If $y = \sin(e^{\log 2x})$, then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{2}$ is

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